Time-resolved thermal mirror method: A theoretical study

Abstract

A general and complete theoretical model of the time-resolved thermal mirror method for the measurement of thermo-optical-mechanical properties of solid materials is developed. The laser-induced temperature profile in a sample and its thermoelastic surface displacement are derived. The center intensity of a probe beam at the detector plane is calculated using the Fresnel diffraction theory. Additionally, simplified models for high and low optical absorption samples are presented, and the suitability of the simplified models is also analyzed. The influence of experimental parameters on the sensitivity of the thermal mirror method is discussed for the optimization of the experimental apparatus. The presented model and the experimental technique can be used to quantitatively determine the physical properties of transparent and opaque solids.

Material characterization

“…The Gaussian laser beam has been proven to be very sensitive [12][13][14] for TM measurements and applicable for a wide absorption coefficient range by using the BLM [12][13][14]. To show the applicability of the top-hat beam excitation and its sensitivity, in Fig.…”

“…Using the integral transform methods [12][13][14][15][16][17][18][19], the solution of heat conduction differential equation for the BLM is…”

“…This method was applied to study optical properties of thin films, semiconductor materials, and characterization of other solid materials [10,11]. Recently, we [12][13][14] theoretically and experimentally demonstrated the applications of photothermally induced nanoscale surface displacement (STL effect) for low [12,14] and high [13,14] optical absorption materials. In these works, the surface displacement was induced by a focused TEM 00 Gaussian excitation laser, and the local surface displacement acted as a concave or convex mirror, namely thermal mirror (TM), to a second TEM 00 laser impinging on the surface deformation.…”

“…In these works, the surface displacement was induced by a focused TEM 00 Gaussian excitation laser, and the local surface displacement acted as a concave or convex mirror, namely thermal mirror (TM), to a second TEM 00 laser impinging on the surface deformation. The surface deformation was dependent on the optical and thermo-mechanical properties of the sample and could be probed by the second laser reflected from it [12][13][14].…”

Photothermal dynamic elastic bending in a semiconductor circular plate induced by a focused laser beam

“…In both employment of the PA and PT effect, the thermoelastic (TE) deformation and electronic deformation (ED), as a prominent deformation of semiconductor samples and the main drive mechanisms for micromechanical structures, should be investigated. A few authors have been investigated optically induced thermoelastic bending in various threedimensional (3D) and two-dimensional (2D) configuration [5][6][7][8], using tightly focused incident source and developing a new class of PT detecting techniques based on deflection of probe laser beam (for example, thermal mirror PT methods), but they didn't include ED phenomena. The TE and ED phenomena were experimentally and theoretically analyzed in some one-dimensional (1D) and 2D micromechanical structures [9][10][11], assuming non-focused optical source.…”